Method for minimizing the error of a measurable quantity

ABSTRACT

In the framework of the method for minimizing the error of a measured variable, particularly a signal to be measured using filtering at variable bandwidth, the bandwidth is regulated on the basis of a physical criterion inherent to the method in such a ways that signal changes not caused by noise are recognized as early as possible.

The present invention relates to a method for minimizing the error of ameasured variable according to the preamble of claim 1.

Typically, measured signals have a noise component in addition to theinformation component. The noise amplitude and/or the noise component ofthe measured signal is typically reduced through low-pass filtering atthe cost of the response time.

For this reason, it is generally necessary to find a compromise betweenlower noise amplitude and shorter response time when evaluating ameasured signal.

According to the related art, filters having a fixed high bandwidth,which have a short response time, are often used; filters of this typehave a high noise amplitude, however. However, by using filters having afixed low bandwidth, the noise amplitude may be reduced, but, as alreadynoted, this procedure results in a longer response time.

Therefore, if a low noise amplitude Is desired in addition to a shortresponse time, a filter having fixed bandwidth, as is taught in therelated art, is not suitable.

Furthermore, methods for minimizing errors, which are based oncontrolling the bandwidth on the basis of fixed predefined values, areknown according to the related art.

In this case, the results may only be optimum for a specific range ofthe signal.

The present invention is based on the object of specifying a method forminimizing the error of a measured variables particularly a signal to bemeasured, which avoids the disadvantages of the related art. Inparticular, a signal output which is optimum in regard to the noise andthe response time is to be ensured.

This object is achieved by the features of claim 1. Further embodimentsand advantages result from the subclaims.

Accordingly, a method for minimizing the error of a measured variable,particularly a signal to be measured using filtering at variablebandwidth, is suggested, in which signal changes not caused by noise,i.e., changes of the information component of the signal, are recognizedas early as possible, the bandwidth being regulated on the basis of aphysical criterion inherent to the method according to the presentinvention.

Preferably, according to the present invention, the band-width isregulated in such a way that the variation of the measured signal barelydoes not exceed a predefined multiple of the intrinsic noise of themeasuring sensor; the bandwidth is preferably regulated by selecting thesuitable filter from a filter bank, which may be a parallel circuit or aseries circuit of filters.

Furthermore, it is possible to perform the filtering in a computer, sothat no filter hardware is necessary. For a method implemented in acomputer, a series circuit may be shown to be advantageous, since theoutput data of a filter may be used for calculating the output data ofthe following filter having lower bandwidth. In this case, a data ratereduction may occur, which saves significant computing time and storagespace. In contrast, in a hardware-based achievement of the object, aparallel circuit provides the most rapid results, since in a seriescircuit the group run times (i.e., the response times) of the filtersmust be summed.

In this case, the intrinsic noises are calculated from the knownspectral noise output densities of the measuring sensor and thebandwidth of the particular filter; advantageously, the difference ofthe observed filter output from a version of the signal whose bandwidthis delimited even more strongly is advantageously observed as avariation of the measured signal.

In particular, starting from a filter of the highest availablebandwidth, smaller and smaller bandwidths are observed until, as alreadyexplained, the current variation of the measured signal is greater thanthe associated intrinsic noise of the measuring sensor. The filterhaving the lowest bandwidth at which, both in this filter and in allfilters having higher bandwidth, the variation of the measured signaldoes not exceed a predefined multiple of the intrinsic noise of themeasuring sensor at this instant, is selected and used for display. Ifno filter output having this property may be established, the filteroutput having the highest bandwidth is selected, since its response timeis the shortest.

Through the method according to the present invention, it is ensuredthat a signal change not caused by noise, i.e., a variation of theinformation component, is recognized as early as possible, since thenext lower filter has a variation in the measured signal which isgreater than the intrinsic noise, so that there must be a signal changenot caused by noise. In addition, the signal change may not berecognized earlier, since all filters of higher bandwidth havevariations so large that they cover the information component of thesignal. The earliest-possible recognition of the change in theinformation component of the signal, which is achievable according tothe present invention, is an important advantage in thermal radiationdetectors or further safety-relevant applications, for example.Furthermore, the method presented here has the advantage that thebandwidth regulation is based on a physical criterion.

In the framework of a variation of the method according to the presentinvention, instead of the above-mentioned criterion, a less restrictivecriterion may be used or, instead of the filter from the filter bank, astandardized linear combination of at least two outputs of the filterbank may be used.

The filters used are preferably low-pass filters.

The method presented here is free of feedback and offers stability basedon a principle.

The present invention will be explained in greater detail in thefollowing for exemplary purposes on the basis of the attached figures.

FIG. 1: shows an illustration of a signal without noise as a function oftime, i.e., an illustration of the information component of the signal;in all further figures, the spectral noise output density of themeasured signals is always 1/Sqrt(Hz);

FIG. 2: shows an illustration of the signal shown in FIG. 1 havingnoises as a function of time, the signal having been conducted through afilter having a bandwidth of 25 MHz;

FIG. 3: shows an illustration of the signal shown in FIG. 1 havingnoises as a function of time, she signal having been conducted through afilter having a bandwidth of 3 MHz;

FIG. 4: shows an illustration of the signal shown in FIG. 1 havingnoises as a function of time, the signal having been conducted through afilter having a bandwidth of 0.4 MHz;

FIG. 5: shows an illustration of the error signal for the signal shownin FIG. 3;

FIG. 6: shows an illustration of the error signal having controlledbandwidth according to the present invention;

FIG. 7: shows an illustration of an exemplary decision procedure usingtwo filters according to the present invention;

FIG. 8: shows an illustration of an exemplary decision procedure usingmultiple filters according to the present invention; and

FIG. 9: shows an illustration of the output signal with controlledbandwidth according to the method according to the present invention.

The idealized case of a signal without noises is illustrated in FIG. 1.The signal performs a jump from 0 to 3 at the instant t=0 and thenremains constant.

FIGS. 2, 3, and 4 provides a realistic illustration. In this case, thesignal from FIG. 1 is illustrated having noises at different bandwidths,the signal being sent through low-pass filters having differentbandwidths for this purpose. The bandwidths are 25 MHz for FIG. 1 [sic;2], 3 MHz for FIG. 3, and 0.4 MHz for FIG. 4. As may be inferred fromFIGS. 2, 3, and 4, the signal having higher bandwidth has a higher noiseamplitude; however, the jump at t=0 is shown more rapidly.

The error signal for a bandwidth of 3 MHz is illustrated in FIG. 5. Theerror signal is the difference between information component, shown herein FIG. 1, and the measured signal after a low-pass filter (having abandwidth of 3 MHz as shown in FIG. 3 here). From the instant t=0 up tothe response time of the low-pass filter, the error corresponds to theentire height of the jump; the response time of the low-pass filter isapproximately 130 seconds in this case. This means that the rapid and/orsignificant signal change (i.e., the jump) is only recognized afterapproximately 130 seconds. Subsequently, as shown in FIG. 3, the errorsignal is dominated by the noise which is characteristic for thebandwidth of the filter.

According to the present invention, a signal may be generated which hasa smaller error than the exemplary 3 MHz filter, because a filter outputhaving higher bandwidth is observed for times shortly and/or directlyafter the jump and a filter output having lower bandwidth is observedfor later instants. In this way, the advantages of higher and lowerbandwidth are advantageously combined.

For example (in the framework of the example shown here), for instantsup to t=200 seconds, a filter having higher bandwidth than 3 MHz may beused, which does have a higher noise amplitude than the 3 MHz filter,but has a shorter response time, so that the error is lower overall. Forinstants over t=1000 seconds, a filter having lower bandwidth than 3 MHzmay preferably be used, which, as already explained, has a lower noiseamplitude than the 3 MHz filter. Therefore, the error resultingtherefrom is lower than the error if a 3 MHz filter is used, if theinformation component remains constant and/or no rapid change occurs, sothat an error is no longer to be expected from the long response time ofthe filter at lower bandwidth.

This is illustrated in FIG. 6. In this case, curve A shows the“improved” error signal which results from the bandwidth regulatedaccording to the present invention. The error signal which correspondsto the use of a 3 MHz filter is illustrated as curve B for comparison.Furthermore, the particular bandwidth (in MHz) used in the filter whichis displayed is illustrated on the basis of curve C, which is assignedto the right Y axis. Accordingly, bandwidths having values between 25MHz and 0.75 MHz are used. The signal obtained through the presentinvention displays an error which corresponds to the error of the 3 MHzfilter in the interval t=360 seconds to t=800 seconds. In the otherregions, the error is significantly lower.

According to the present invention, the bandwidth is regulated in such away that the variation of the observed signal barely does not exceed apredefined multiple of the intrinsic noise of the measuring sensor. Thefollowing procedure is preferably used to regulate the bandwidth of thefilter: the absolute value of the distance of the observed filter outputto a second filter output having lower bandwidth is analyzed. This meansthat the second filter having lower bandwidth represents the measuredsignal without noise for the observed filter. If the distance betweenthe observed filter output and the second output of the filter havinglower bandwidth is so small that the distance may be interpreted asrandom noise of the observed filter output, the observed filter may beused for display. Such a filter will be referred to as a permittedfilter in the following.

If the distance between the observed filter output and the second outputof the filter having lower bandwidth is so large that it may not beinterpreted as random noise, a significant change of the informationcomponent is then recognized. This filter is not a permitted filter.This results in the use of a filter having higher bandwidth, since inthis case a lower response time will minimize the error. At least threefilters having different bandwidths are necessary to perform the method.

A multiple of the standard deviation σ of the intrinsic noise of themeasuring sensor is used as the threshold value for the absolute valueof the distance of the observed filter output to a filter output oflower bandwidth, because of which the signal analysis is based on aphysical criterion inherent in the measurement system. This avoids afilter being sought out on the basis of arbitrary parameters and/orparameters generated outside the measurement system and thus beingdisplayed. If the distance between the observed filter output and afilter output of lower bandwidth is within the setpoint interval, thenthis distance corresponds to the random noise of the observed filteroutput.

An exemplary decision procedure of this type is illustrated in FIG. 7.Curve A shows the signal obtained from a 3 MHz filter and curve B showsthe signal obtained from a 1.6 MHz filter; curves C and D represent aband around the signal of the 1.6 MHz filter. This band corresponds to+/−5 σ of the intrinsic noise of the 3 MHz signal, so that theprobability that the 3 MHz signal will leave the band at a constantinformation component is negligibly small.

According to the present invention, it is possible to observe only theupper, independent halves of the noise spectrum in order to eliminatethe influence of the noise of the filter of lower bandwidth.

Curve E represents the curve of a logical signal which shows that theabsolute value of the distance of the 3 MHz signal to the 1.6 MHz signalis less than 5 σ of the 3 MHz signal. This logical signal is thus thesignal which displays whether and when an observed filter is a permittedfilter and may be used for display.

As may be seen in FIG. 7, in the interval t=70 seconds to t=360 seconds,the 3 MHz signal leaves the 5 σ band around the 1.6 MHz signal. Thismeans that according to the present invention, the 3 MHz signal betweent=70 seconds and t=360 seconds may not be used for display, since thedistance between the observed filter output and the output of the filterhaving the lower bandwidth of 1.6 MHz is so large that it may not beinterpreted as random noise.

FIG. 8 shows the method for multiple filters of different bandwidths forexemplary purposes. In this case, the bandwidths of the filters are 25,12, 6, 3, 1.6, and 0.8 MHz. In the figure, the logical signalscorresponding to these filters are plotted as curves A, B, C, D, E, andF, respectively. Furthermore, the bandwidth of the filter which is thepermitted filter having the smallest bandwidth is plotted as curve G(curve G is assigned to the right Y axis), all filters having higherbandwidth also being permitted filters.

FIG. 9 shows the output signal for controlled bandwidth according to thepresent invention. It may be seen from the figure that the displayedsignal for controlled bandwidth follows the jump at t=0 rapidly; inaddition, the noise becomes lower with increasing time.

The method presented here may be applied, for example, in an electronicbalance, so that a usable display may be provided directly after aweight is laid on the balance. This is not yet very precise, butnonetheless immediately represents a value which corresponds to thecurrent weight and not the prior display. If the weight remains on thebalance longer, then the displayed result becomes more precise as timepasses.

Furthermore, the method according to the present invention may be usedto display the signals which are generated by a device for measuringsmall gas concentrations, such as 2 photometer having thermal detectors.

The method according to the present invention has the advantage that thebandwidth regulation is based on a physical criterion. If the spectralnoise output density of the signal source is known, then the distancecriterion for every filter may be derived therefrom. Preferably, thevalue 5 σ is selected, but other values or multiples of a are alsoconceivable. Fixing an arbitrary threshold value, which may not besuitable for a specific signal curve, is therefore excluded.

In addition, the data quantity required is reduced in comparison to therelated art by the method according to the present invention. If, forexample, the signals coming to the display are stored, then at lowerbandwidths, correspondingly few data points are also necessary.According to the present invention, rapid signal changes are registeredimmediately if the information component stands out of the noise. For aninformation component which changes only slowly, only a few averagevalues are stored over long times. The method does not harm the samplingtheorem for signal components which stand out of the noise. Therefore,all information which the measuring sensor may register from the signalcomponent may also be stored.

A further advantage of the method is that it is inherently stable, sincethere is no feedback. The application of the method in the case that thespectral noise output density of the signal is constant and is largelyindependent of the signal amplitude has been shown to be especiallyadvantageous. This is the case in wide ranges for signals from sensorswhich are not quantum detectors, e.g., strain gauges, platinum andnickel thermistors, NTCs and PTCs, semiconductor temperature sensors,thermocouples, magnetoresistors, piezoresistive sensors, thermalradiation detectors, etc. In these cases, the noise amplitude is afunction of the square root of the bandwidth, so that the regulation ofthe bandwidth is simple to perform, since in this case the distancecriterion is especially simple, since the noise amplitude is smaller bythe factor a if the bandwidth is reduced by the factor a*a.

1. A method for minimizing the error of a measured variable,particularly a signal to be measured, using filtering at variablebandwidth, comprising the step of regulating the bandwidth on the basisof a physical criterion inherent to the method in such a way that signalchanges not caused by noise are recognized as early as possible.
 2. Themethod according to claim 1, wherein the bandwidth is regulated in sucha way that the variation of the signal does not substantially exceed apredefined multiple of the intrinsic noise of the measuring sensor. 3.The method according to claim 2, wherein the intrinsic noise iscalculated from the known spectral noise output density of the measuringsensor and the bandwidth of the filter.
 4. The method according to claim1, wherein the difference of the signal from a version of the signalwhose bandwidth is delimited more strongly is observed as a variation ofthe signal.
 5. The method according to claim 1, wherein a suitablefilter is selected from a filter bank in the framework of the bandwidthregulation.
 6. The method according to claim 5, wherein a standardizedlinear combination of at least two outputs of the filter bank is usedinstead of an individual filter from the filter bank.
 7. The methodaccording to claim 5, wherein the filter bank is a parallel circuit or aseries circuit of filters.
 8. The method according to claim 5, whereinlow-pass filters are used as filters in the filter bank.
 9. The methodaccording to claim 4, wherein an absolute value of the distance of anobserved filter output to at least one further filter output havinglower bandwidth is observed and, if the distance between the observedfilter output and the output of the at least one filter having lowerbandwidth falls below a threshold value, which is a predefined multipleof the intrinsic noise of the measuring sensor, the observed filter isused to display the signal; and if the distance between the observedfilter output and the output of the at least one filter having lowerbandwidth exceeds a threshold value, a significant change of theinformation component in the signal is recognized and a filter having atleast one of higher bandwidth and lower response time is used, whoseoutput is displayed.
 10. The method according to claim 9, wherein thefilter which has the lowest bandwidth of all filters whose outputsignals do not exceed the threshold value is used to display the signalto be measured.
 11. The method according to claim 9 wherein thethreshold value is a multiple of the standard deviation of the intrinsicnoise of the measuring sensor.
 12. The method according to claim 1,further comprising the steps of receiving the signal to be measured froma device selected from the group consisting of strain gauges, PT100sensors, thermocouples, piezoresistive sensors, and thermal radiationdetectors, and displaying the measured variable.
 13. The methodaccording to claim 5, wherein the filter bank is a series circuit offilters.